This is a Test of Mathematics Solution Subjective 70 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
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Suppose that all roots of the polynomial equation
= 0 are positive real numbers.
Show that all the roots of the polynomial are equal.
If the roots are , , and .
then , , and = 1
& + + + = 4.
Now all of , , and are positive so AM-GM inequality is applicable.
Now we know equality in AM-GM occours if all the numbers are equal.So , , and are all equal.